Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T19:18:02.075Z Has data issue: false hasContentIssue false
  • English
  • Français

Central extensions and Schur’s multiplicators of Galois groups

Published online by Cambridge University Press:  22 January 2016

Katsuya Miyake
Katsuya Miyake*
Affiliation:
Department of Mathematics, Faculty of General Education, Nagoya University, Nagoya 464, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

When he developed the theory of central extensions of absolute abelian fields in [1], Fröhlich clearly pointed out a role of Schur’s multiplicators of the Galois groups in algebraic number theory. Another role of them was to be well known when the gaps between the everywhere local norms and the global norms of finite Galois extensions were cohomologically described by Tate [10]. The relation of two roles was investigated by Furuta [2], Shirai [9], Heider [3] and others.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 90 , June 1983, pp. 137 - 144
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[ 1 ] Fröhlich, A., On fields of class two, Proc. London Math. Soc. (3), 4 (1954), 235–236.Google Scholar
[ 2 ] Furuta, Y., On nilpotent factors of congruent ideal class groups of Galois extensions, Nagoya Math. J., 62 (1976), 13–28.Google Scholar
[ 3 ] Heider, F.-P., Strahlknoten und Geschlechterkörper mod m, J. reine angew. Math., 320 (1980), 52–67.Google Scholar
[ 4 ] Hoehschild, G. and Nakayama, T., Cohomoiogy in class field theory, Ann. of Math., 55 (1952), 348–366.Google Scholar
[ 5 ] Hoehschild, G. and Serre, J.-P., Cohomoiogy of group extensions, Trans. Amer. Math. Soc, 74 (1953), 110–134.Google Scholar
[ 6 ] Masuda, K., An application of the generalized norm residue symbol, Proc. Amer. Math. Soc, 10 (1959), 245–252.CrossRefGoogle Scholar
[ 7 ] Miyake, K., On the structure of the idele group of an algebraic number field, Nagoya Math. J., 80 (1980), 117–127.CrossRefGoogle Scholar
[ 8 ] Serre, J.-P., Modular forms of weight one and Galois representations, in : Algebraic Number Fields, ed. by Fröhlich, A., Academic Press, London: New York: San Francisco, 1977.Google Scholar
[ 9 ] Shirai, S., On the central class field mod m of Galois extensions of an algebraic number field, Nagoya Math. J., 71 (1978), 61–85.Google Scholar
[10] Tate, J., Global class field theory, in: Algebraic Number Theory, ed. by Cassels, J. and Fröhlich, A., Academic Press, London and New York, 1967.Google Scholar